Journal of Operator Theory

Volume 40, Issue 2, Fall 1998 pp. 357-372.

Characteristic matrix of the tensor product of operators

Authors: Hideki Kosaki
Author institution: Graduate School of Mathematics, Kyushu University, Fukuoka, 810, Japan

Summary: The characteristic matrix of the tensor product of two Hilbert space operators is analyzed. The case where operators are not necessarily closable is also considered, and we determine $(i)$ the closure of the graph of the algebraic tensor product $T_1 \otimes_{\rm alg} T_2$, $(ii)$ the maximal closable part of $T_1 \otimes_{\rm alg} T_2$ in the sense of P. Jørgensen ([1]).

Keywords: Characteristic matrix, maximal closable part, tensor product of unbounded operators

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